NBER WORKING PAPER SERIES

INTERNAL DEBT CRISES AND SOVEREIGN DEFAULTS

Cristina ArellanoNarayana R. Kocherlakota

Working Paper 13794http://www.nber.org/papers/w13794

NATIONAL BUREAU OF ECONOMIC RESEARCH1050 Massachusetts Avenue

Cambridge, MA 02138February 2008

We thank Katya Kartashova and Jacek Rothert for research assistance, and participants at seminarsat the Federal Reserve Banks of New York City and Philadelphia for their comments. The opinionsexpressed herein are those of the authors and not necessarily those of the Federal Reserve Bank ofMinneapolis, the Federal Reserve System, or the National Bureau of Economic Research.

NBER working papers are circulated for discussion and comment purposes. They have not been peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies officialNBER publications.

© 2008 by Cristina Arellano and Narayana R. Kocherlakota. All rights reserved. Short sections oftext, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit,including © notice, is given to the source.

Internal Debt Crises and Sovereign DefaultsCristina Arellano and Narayana R. KocherlakotaNBER Working Paper No. 13794February 2008JEL No. F34,G33

ABSTRACT

In this paper, we use data from developing countries to argue that sovereign defaults are often causedby fiscal pressures generated by large-scale domestic defaults. We argue that these systemic domesticdefaults are caused by shocks best interpreted as being non-fundamental. We construct a model thatis consistent with these observations. The key ingredient of the model is that it is impossible to liquidatelarge amounts of entrepreneurial assets. This restriction generates the possibility of a domestic coordinateddefault crisis, in which domestic borrowers find it optimal to default because all other borrowers arealso defaulting. We conclude that avoiding sovereign defaults requires better internal institutions, notbetter external ones.

Cristina ArellanoDepartment of EconomicsUniversity of Minnesota271 19th Avenue SouthMinneapolis, MN 55455arellano@econ.umn.edu

Narayana R. KocherlakotaDepartment of EconomicsUniversity of Minnesota271 19th Avenue SouthMinneapolis, MN 55455and NBERnkocher@econ.umn.edu

1. IntroductionIn developing countries, governments face occasional sharp increases in the interest

rates that they pay as borrowers. These sovereign debt crises often (but not always) precede

debt restructuring or actual default. In this paper, we provide a novel explanation of these

events.

We begin by providing new types of evidence about the sources of sovereign debt

crises. We use data on sovereign and domestic private sector interest rates to show that

ex-ante measures of domestic private sector default risk are positively correlated over time

with sovereign default risk. We also demonstrate that sovereign defaults are often associated

with large numbers of domestic defaults, such as bank insolvencies and non-performing bank

loans. Thus, sovereign defaults and sovereign debt crises are external problems that coincide

with similar problems in internal financial markets.

This analysis does not identify the basic sources of these twin problems. We use two

types of evidence to address this issue. First, we look at the temporal connection between

internal debt crises, which are generated by large-scale private sector loan defaults, and

sovereign defaults. We show that in countries that experience both private and sovereign

default crises, the private internal debt crisis typically precedes the sovereign default. Thus,

problems in internal financial markets precede external problems for sovereign borrowers. We

also show that internal debt crises put strong fiscal pressures on government, because they

involve large fiscal transfers to lenders such as bank depositors and owners.

To get more detailed causal evidence, we turn to the particular case study of Indonesia

in 1997. We document that a fall in the value of the Thai baht triggered domestic bank

loan defaults in Indonesia. There were few connections between the Thai and Indonesian

economies; hence, the basic shock seems to be non-fundamental in nature. Here, as is true

more generally, the bank loan defaults led to large fiscal transfers to banks and consequently

to sovereign default.

We reach the following conclusions from our examination of the evidence. Non-

fundamental shocks have the capability to generate large-scale domestic defaults. Such de-

faults cause the government’s net tax collections to fall. Domestic governments then face fiscal

pressures that can possibly lead to defaults. Given this chain of events, sharp increases in

interest rates on sovereign and domestic loans are attributable to increases in the probability

of the underlying non-fundamental shocks.

In the remainder of the paper, we build a model that rationalizes why these events

occur, and why developing countries are especially prone to them. Our model has the fol-

lowing elements. There is a benevolent government in a small open economy which borrows

from foreign risk-neutral lenders to buy public goods. At the same time, a small number of

domestic risk-averse entrepreneurs borrow from domestic risk-averse lenders to buy capital

goods for use in a productive investment opportunity. The domestic entrepreneurs’ invest-

ment returns are a binary random variable that may equal zero with positive probability;

returns are, ex-post, known only to the entrepreneur. The government imposes lump-sum

taxes on these domestic lenders in order to finance its repayments to the foreign lenders.

Liquidation plays a key role in the model. The entrepreneur’s capital goods can

be liquidated to become consumption goods, but liquidation involves a social loss.1 We

focus on equilibrium loan contracts which specify repayment/liquidation as a function of the

entrepreneurs’ declarations of success or failure. In an equilibrium contract, a successful

entrepreneur will make a payment to the lender without any liquidation. In contrast, an

unsuccessful entrepreneur will liquidate some of his capital, and use that to make a payment

to the lender. Thus, equilibrium contracts look like standard debt contracts, with default

provisions.

We document that in Indonesia in 1997, liquidation of a given debt took much longer

because many debts were simultaneously in default. This observation motivates our key as-

sumption: there is an upper bound on the total amount of capital that can be liquidated.

Hence, if many entrepreneurs default, the lender can only liquidate a small amount of capital

from each of them. We show that if the upper bound on aggregate liquidation is suffi-

ciently tight, then a positive probability non-fundamental shock (a sunspot) can generate

what we term a coordinated default crisis. In this crisis, domestic entrepreneurs use the non-

fundamental shock to coordinate on a default decision, even if they have been successful. The

crisis is generated by a simple self-fulfilling belief: If all entrepreneurs know that all other

1This approach to designing an optimal loan repayment contract with default is similar to that taken byDiamond (1984) and Rampini (2005).

2

entrepreneurs are going to default, then they all know that they face a small sanction for

doing so.

The massive default means that the domestic lenders cannot pay their taxes. Without

these tax payments, the sovereign cannot repay the foreign lender in full. Indeed, in these

crises, it may well be optimal (for risk-sharing reasons) for the foreign lender to make transfers

to the sovereign. The government will then give those transfers to the domestic lenders.

Thus, our model is consistent with all of our earlier observations. Domestic default

crises and sovereign default crises are tightly linked in the model and in the data. In the

model, as in the data, non-fundamental shocks are responsible for the crises, which can

feature large transfers from governments (and foreign lenders) to domestic lenders. As well,

we prove that in our model, the returns to both domestic debt and sovereign debt rise when

non-fundamental shocks become more likely. In this sense, domestic debt and sovereign debt

returns are correlated in our model, just as we found that they are in the data.

In the data, sovereign defaults and internal debt crises are often associated with large

real exchange rate depreciations. Our model is consistent with this phenomenon. We think of

the entrepreneurs’ projects as producing nontradables. At the same time, the domestic lender

has an outside opportunity to invest in the production of tradables. A real exchange rate

depreciation makes the outside opportunity look more attractive. It follows that equilibrium

contracts have to feature larger liquidations from defaulting entrepreneurs to compensate the

lender. It is exactly these large liquidations that generate the possibility of default crises

according to our theory.

The existence of coordinated default crises in our model is an example of what is called

an implementation problem in the optimal contracting literature. In our model, an equilibrium

contract generates a reporting game between entrepreneurs by specifying repayments and

liquidations as a function of the joint reports of the entrepreneurs about their outcomes. In

one equilibrium of this game, both entrepreneurs tell the truth, and induce a constrained

Pareto optimal allocation of resources. The key property of our model is that, under some

parameter settings, the equilibrium contract allows for a second equilibrium in the reporting

game in which both lie. The resultant equilibrium outcome is not constrained Pareto optimal.

There is a large literature on implementation problems in contractual design. Our

3

paper is most related to the recent contributions of Bassetto and Phelan (2006) and Bond

and Hagerty (2007). As in our paper, their implementation problems emerge because society’s

ability to provide a negative incentive to a given player depends on the number of players

who are also supposed to receive such incentives. More concretely, Bassetto and Phelan

hypothesize that the probability of any given taxpayer’s being audited falls if all taxpayers

claim to have low incomes. Under this hypothesis, there is an equilibrium in which all

taxpayers choose to default on their tax obligations, regardless of their true incomes. Bond

and Hagerty assume that resources for crime enforcement cannot be adjusted in response to

the level of crime. Again, this technological restriction generates a second inferior equilibrium

with large amounts of crime.

Why do we need a theory of sovereign debt crises? Some sovereign default episodes

can be rationalized using movements in output or other fundamentals. (See Arellano (2007)

for such an account of the recent sovereign default episode in Argentina.) Nonetheless, it is

widely recognized that the connection between sovereign defaults and economic fundamentals

is, at best, loose.2 Without a convincing fundamental explanation available, other economists

following Calvo (1988) have turned, as we have, to a non-fundamental one. In a series

of policy papers about sovereign debt crises, Sachs (1997), Krugman (1998), Chari and P.

Kehoe (1998), Fischer (1999), and Krueger (2002) attribute them to panics or more general

forms of coordination failures among foreign lenders. The rough idea is that, without any

change in fundamentals, all foreign lenders change their beliefs about other lenders’ behavior.

This change in beliefs generates a bank run of sorts on the sovereign borrower.3

We see two major problems with this external debt crisis explanation of sovereign debt

crises. The first is a conceptual one. The external debt crisis explanation emphasizes the

behavior of foreign lenders. But sovereign debt crises do not affect all borrowing countries -

just developing ones. The external debt crisis theory does not tell us why this difference in

the characteristics of the borrower should affect the prevalence of crises. Our theory does:

2For example, Tomz and Wright (2006) document that 38 percent of default episodes since 1820 haveoccurred when countries had GDP levels above trend.

3Cole and T. Kehoe (2000) go beyond purely verbal intuitions, and provide models of this phenomenon.They emphasize that sovereign debtors might default when foreign lenders refuse to roll over debt becausethey believe other lenders may also refuse to do so.

4

developing countries cannot liquidate enough capital when large numbers of entrepreneurs

default.

The second problem is an empirical one. Above, we document that sovereign defaults

are systematically related to large-scale private domestic defaults within the borrowing coun-

try. More specifically, we show that default risk in loans made to a government is positively

associated with default risk in the loans made among domestic private lenders and that do-

mestic debt crises largely precede sovereign debt crises. Again, the external debt crisis theory

tells us nothing about this phenomenon. Our theory is deliberately designed to rationalize

it.

The distinction between our new theory and the existing one is not of purely academic

interest. The above-cited policy papers all agree that there is a need for the International

Monetary Fund to adopt policies that curtail these panics among external lenders. (They do

disagree on the exact policy that this agency should follow). When internal crises are the key

problem, the IMF and other international agencies really play no useful role. According to our

theory, developing countries have sovereign debt problems because their process of domestic

debt repayment is highly strained when faced with large numbers of domestic defaults. We

model this limitation as purely technological. More realistically, developing countries can

achieve better outcomes by improving their financial institutions to deal with potential large-

scale defaults.

2. EvidenceIn this section, we provide evidence that sovereign debt crises are triggered by increases

in the probability of private sector defaults. We first document that sovereign default risk

and private default risk move together in developing countries in both an ex-ante and ex-post

sense. From an ex-ante perspective, we show that the dollar spreads on international sovereign

bonds have a tight correlation to dollar domestic lending spreads charged to private borrowers.

From an ex-post perspective, we show that episodes of international sovereign defaults largely

coincide with episodes of large domestic private defaults.

Second, we find that these twin debt crises begin with problems in the private sector

that pass into the sovereign government. We document that internal debt crises typically

5

pre-date sovereign defaults and that these episodes are characterized by large transfers from

the government to the private sector. Finally, we discuss the case of Indonesia in 1997. There,

non-fundamental pressures generated a breakdown in the domestic banking system and vast

private defaults. The internal debt crisis then led the government to default on its sovereign

debt, due to fiscal pressures coming from its bailing out banks.

A. Sovereign Default and Private Default

We first look at the co-movement of the probability of default for sovereign govern-

ments and private borrowers in emerging markets. Our data set consists of monthly data for

eighteen emerging markets: Argentina, Brazil, Chile, Colombia, Ecuador, Indonesia, Korea,

Malaysia, Mexico, Nigeria, Panama, Peru, Philippines, Poland, Russia, Thailand, Ukraine,

and Venezuela. Our choice of countries is guided by data availability — the countries we con-

sider belong to the set included in J. P. Morgan’s EMBI+, to the emerging markets considered

in Kaminsky and Reinhart (1998), or both. Our measure for sovereign default probabilities4

is the EMBI+ spread for each country, which is the difference between the yield of dollar

denominated bonds relative to the yield of similar U.S. government bonds.5

Table 1: Correlations of Sovereign and Private Default Risk

Argentina 0.81 Nigeria 0.47Brazil 0.38 Panama 0.44Chile 0.45 Peru 0.69Colombia 0.08 Philippines -0.40Ecuador 0.37 Poland -0.48Indonesia 0.29 Russia 0.47Korea 0.54 Thailand 0.54Malaysia 0.18 Ukraine 0.41Mexico 0.85 Venezuela 0.33

4Treating the EMBI+ spread in this way ignores other possible sources of changes in expected returns.These include variations in liquidity or variations in country-specific betas relative to the world marketportfolio.

5Five of these countries (Chile, Indonesia, Korea, Malaysia and Thailand) do not have EMBI+ spreads.For these countries, we use spreads of an alternative government bond, instead of the EMBI+ spread. Thedetails are in Appendix A.

6

For the private sector, we need a measure that captures the probability of default of

domestic private borrowers on their loans. To this end, we use the dollar lending rates of

domestic banks relative to the yield of United States Treasury bills. In countries for which

domestic dollar rates are not available, we use the local currency spread between the average

lending rate and the average deposit rate to proxy default probabilities. Table 1 shows that the

correlations of sovereign and private default risk are strongly positive for 15 of the countries

in the sample.6 Figure 1 further illustrates the strong co-movement between sovereign default

risk and private default risk and that spikes in sovereign default probabilities are generally

accompanied by spikes in the domestic private default probabilities.7

Thus, from an ex-ante perspective, sovereign and private loan default probabilities

fluctuate together over time. We now present evidence of ex-post covariation. We show that

since 1980, episodes of sovereign defaults largely coincide with periods of internal debt crises.

To date sovereign defaults, we use the Standard and Poor’s classification and include defaults

on both foreign currency bank debt and foreign currency bond debt. To proxy internal debt

crises, we use the commonly used dates of banking crises from Caprio and Klingebiel (2003).

As they document, these crises are characterized by widespread domestic defaults with large

increases in non-performing loans and collapses of banks.8

Table 2 shows that from 1980-2003 there have been 22 sovereign defaults in our sample

of emerging markets and 19 of those have also involved an internal debt crisis.9 These coun-

tries have also experienced 14 additional internal debt crises without a sovereign default. The

unconditional default probability in any year is equal to 6.9% and the unconditional internal

debt crisis probability is equal to 8.8% in our sample. Sovereign defaults also occur together

6The correlations between EMBI+ spreads and nominal lending rates are strongly positive for all countriesin the sample including Colombia, Phillipines and Poland. This finding is similar to that of Mendoza andYue (2007). They show that the correlation between EMBI+ spreads and firm financing costs are stronglypositive. Their measure of the latter is in terms of domestic currency, and so includes an own-countryinflationary component.

7Appendix A contains the description and sources of all the data.8Only two of the banking crises described by Caprio and Klingebiel (2003) in their paper feature bank

runs. Neither of these is included in our subsample of countries and crises.9Importantly, the concurrence of internal debt crises and sovereign defaults appears greater than for the

more studied twin crises of balance of payments and internal debt. Kaminsky and Reinhart report thatfrom 1975 to 1995 in a sample of 20 countries, from the 57 balance of payment crises, only 19 of them wereaccompanied by an internal debt crisis.

7

Brazil

0

10

20

30

F-98 F-00 F-02 F-04 F-06

20

40

60

Mexico

0

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J-98 J-00 J-02 J-04 J-06

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Nigeria

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J-98 J-00 J-02 J-04 J-06

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Venezuela

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J-98 J-00 J-02 J-04 J-06

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Colombia

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J-99 J-01 J-03 J-05

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Phililppines

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J-98 J-00 J-02 J-04 J-06

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Government default risk -- left axis

Korea

-4

-2

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F-96 F-98 F-00 F-02 F-04 F-06

-3

-1

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Thailand

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F-97 F-99 F-01 F-03 F-05 F-07

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Malaysia

-2

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Chile

-6-4-20246

M-92 M-96 M-00 M-04

0

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Private default risk-- right axis

Argentina

0

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D-97 D-99 D-01

0

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Peru

0

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J-98 J-00 J-02 J-04 J-06

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Russia

0102030405060

F-98 F-00 F-02 F-04 F-06

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Ukraine

0

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S-01 S-03 S-05

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Ecuador

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F-99 F-01 F-03 F-05 F-07

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Poland

0

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M-02 M-04 M-06

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Panama

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Indonesia

0

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S-00 S-01 S-02 S-03

0

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8

Figure 1: Sovereign and Private Sector Default Risks Over Time

8

with internal debt crises in a broader sample of all 93 middle income countries. We find that

39 out of the 63 sovereign defaults that occurred in these countries have been accompanied

by internal debt crises. Appendix A contains the countries and dates for sovereign defaults

and internal debt crises in our sample of emerging markets.

Table 2: Sovereign Defaults and Internal Debt Crises from 1980-2003

Only Sovereign Only Private Both

Emerging markets 3 14 19

Middle income countries 24 43 39

B. Causal Channel

We have documented a positive association between domestic default risk and sovereign

default risk and that two events - domestic private defaults and sovereign defaults - tend

to occur together. However, this evidence does not speak to the issue of causation. In

this subsection, we show that cross country evidence points towards domestic private sector

defaults causing sovereign defaults.

We find that the typical case evolves as follows. First, an internal debt crisis occurs

in the country, characterized by large levels of non-performing loans and many failing local

banks. The government then transfers resources to the banking sector. Subsequently, the

government defaults on its sovereign international debt. This timing of events in the cross

section of countries suggests that the origin of the twin debt crises are the private domestic

defaults.

One way to see the imprint of this basic story is that in our sample of emerging

markets, internal debt crises largely predate sovereign defaults. >From the 19 joint crises,

the internal debt crisis started at least a year before the sovereign default in 11 cases, started

after the sovereign default in 4 cases and occurred contemporaneously during the same year

in 4 cases. Internal debt crises are very costly for the government, reaching in some cases over

9

50% of GDP. The average fiscal cost from the internal debt crises in the sample of emerging

markets is 19.7% of GDP.

To get more detail, we turn to a specific case study: Indonesia in 1997. The Indonesian

crisis illustrates how domestic private defaults can generate sovereign defaults. We further

find that the deep internal debt crisis in Indonesia was generated largely by non-fundamental

forces.

In June 1997, the banking sector in Indonesia was largely solvent, with a surplus of

assets compared to liabilities of 8%.10 On July 2, 1997, the Thai government allowed the baht

to float, and it depreciated dramatically. Thailand has few economic links with Indonesia.11

Despite this lack of links, an enormous internal debt crisis began to unravel in Indonesia

soon after the baht’s depreciation. By October of 1997, 50 banks were considered insolvent,

and by March of 1998, that number increased to 154 banks. These banks had large levels of

non-performing loans, exceeding in some cases 90% of the loans, and accounted for half of

the banking system. By March 1999 the banking system had a deficit of assets compared to

liabilities of -34%.12

The large private sector defaults and bank failures generated a large pressure for the

government to transfers funds to banks. By January of 1998, the government had provided

liquidity to banks that amounted to 7% of Indonesia’s 1997 GDP. And in August of 1998,

the government defaulted on its international bank debt, in large part because of the fiscal

burden associated with bailing out the banks.

C. Summary

We have shown that private sector default probabilities co-vary with sovereign default

probabilities. We have also presented evidence that the causation runs from the private

10See Enoch, Baldwin, Frecaut, and Kovanen (2001) for further discussion on Indonesian internal debtcrisis.11For example, Kaminsky and Reinhart (2000) find that trade linkages are too weak for them to explain

the contagion in Asia. Thailand exports to Indonesia, Korea, Malaysia, and Philippines combined are only8% of Thailand’s exports.12Despite the prominent role of foreign currency debt in theoretical models of financial crises, most of the

empirical firm level evidence has not found a significant effect of currency mismatch. Beakley and Cowan(2008) find that firms holding dollar debt do not invest less than firms holding peso debt following largedevaluation episodes in Latin America. Luengnaruemitchai (2003) finds a similar result for Asian firmsduring the Asian Crisis.

10

sector to the sovereign, as widespread private sector defaults generate fiscal transfers from

the sovereign, which lead to sovereign default. At least in Indonesia in 1997, the source of

the private sector defaults is manifestly non-fundamental. In what follows, we construct a

model that rationalizes this chain of events.

3. The Model: Environment and EquilibriumIn this section, we describe a simple model of domestic and foreign lending. We then

characterize equilibrium contracts in this setting.

A. Environment

We consider a small open economy. Within this country, there is a domestic lender,

who is endowed with two units of investment goods in period 1. The domestic lender has a

technology that converts these goods into 2R units of consumption goods in period 2, where

R > 1; this technology will serve as the lender’s outside option. We think of this domestic

lender as being any agent within the country who contributes resources to investment. In

this sense, bank depositors are domestic lenders.

There are also two entrepreneurs. Entrepreneur n has a technology that converts 1 unit

of investment goods in period 1 into Rn units of consumption goods in period 2. Here, Rn,

n = 1, 2, are i.i.d. random variables, with realizations that are determined at the beginning

of period 2. With probability (1 − p), Rn equals RH > R > 0 and with probability p, its

realization is R0 = 0. There is a key informational restriction in this setting: the realization

of Rn is privately known to entrepreneur n, and the entrepreneur has the ability to consume

the project return secretly.

Entrepreneurs also have a technology that liquidates invested capital in period 2. If

L units of capital are liquidated, then it generates δL units of consumption goods, 0 ≤ δ ≤1. Entrepreneurs, but not lenders, derive consumption benefits from the (1 − L) units of

unliquidated capital. Those consumption benefits equal BE(1 − L) units of consumption,

where BE > 1. Hence, there is a social loss associated with liquidation and repayment of

loans using capital. We assume throughout that 0 ≤ L ≤ 1, so that liquidation is boundedby the entrepreneur’s total capital investment.13

13We refer to the entrepreneurs’ liquidating their capital. We can just as easily interpret the "capital" in

11

An entrepreneur has a utility function uE over total consumption, which includes the

consumption benefits from unliquidated capital. The domestic lender has a utility func-

tion uL over consumption goods. The utility functions uL and uE satisfy the properties

u0L, u0E,−u00L,−u00E > 0, and uL(0) = uE(0) = 0. Both functions exhibit non-increasing ab-

solute risk aversion. The consumptions of the lender and entrepreneurs of every good are

restricted to be non-negative.

In addition to the three agents, there is a government. The government is able to

borrow and lend from foreign lenders at a gross rate of return RFOR > 1. The government

needs to create G amount of public goods in period 1. It does so by borrowing G units of

consumption goods in period 1 from an international debt market, and then transforming

them, one for one, into the required public goods. It repays this loan in period 2, using taxes

τ collected from the domestic lender.

The key to the model is that we impose a non-trivial upper bound on aggregate

liquidation. We are motivated to adopt this assumption by observations from Indonesia

in 1997-99. Indonesia had two separate systems designed to handle liquidations of failing

firms. Initially, it had only a court system. But the courts quickly became overloaded

with bankruptcy cases to resolve. As a response, the Jakarta Initiative Task Force (JITF)

was created as a way to allow for less formal workouts. However, both the court system

and the JITF had very limited success in expediting the process of non-performing loans.

By October 1999, only 42 bankruptcy cases were settled through the Courts, out of the

112 filed cases. Only 27 cases were settled through JITF, out of the 350 files cases. The

general sentiment was that "the organizational capacity and human resources of the court

appeared insufficient to meet the extraordinary demand for debt settlement posed by massive

bankruptcies" (Insolvency Systems in Asia: An Efficiency Perspective, OECD Report, 2001,

p. 57).

Given these observations, we assume that total liquidation is bounded from above by

ξ, where 1 ≤ ξ < 2. This constraint says that if both entrepreneurs default, it is not possible

to take more than ξ/2 from either of them. As we shall see, this upper bound on liquidation

lies at the heart of the model.

the model as being "collateral goods", as in Kocherlakota (2001) and Kocherlakota and Shim (2007).

12

Note that the model is designed to be as simple as is possible, given the facts that we

want to confront. We need a government and a foreign lender, because we want to include

international sovereign borrowing in the model. We need a domestic lender, because we want

to include private domestic borrowing/lending in the model. Finally, we need more than one

entrepreneur in the model in order to get the possibility of a coordination problem of some

kind.

B. Equilibrium

In period 2, the two entrepreneurs simultaneously announce their returns. There are

four possible outcomes for these announcements. At the beginning of period 1, the government

chooses a tax schedule (τ s)s∈{0,1,2}, where τ s is the domestic lender’s tax payment when s

entrepreneurs claim to have high returns. The government’s goal is to maximize a weighted

sum of the expected utilities of the entrepreneurs and the domestic lender.

After the government commits to a tax schedule, the domestic lender commits to a loan

contract (F,L) at the beginning of period 1. Under this contract, if in period 2 entrepreneur

1’s announced return is Ri and entrepreneur 2’s announced return is Rj, then entrepreneur

1’s repayment is Fij and entrepreneur 1’s liquidation is Lij. Symmetrically, entrepreneur 2’s

repayment is Fji and entrepreneur 2’s liquidation is Lji. The upper bounds on liquidation

and lower bounds on consumption of each good imply that for all (i, j) in {H, 0}2:

Fij ≤ Ri

1 ≥ Lij ≥ 0(1)

Lij + Lji ≤ ξ

The Revelation Principle says that, without loss of generality in terms of equilibrium out-

comes, we can focus on loan contracts that satisfy the incentive-compatibility condition:

(1− p)[uE(BE (1− LHH) +RH − FHH)] + p[uE(BE (1− LH0) +RH − FH0)](2)

≥ (1− p)[uE(BE (1− L0H) +RH − F0H)] + p[uE(BE (1− L00) +RH − F00)]

Intuitively, entrepreneurs send simultaneous announcements of their returns to the lenders.

13

These incentive-compatibility conditions guarantee that truth-telling is a Bayesian-Nash equi-

librium of this reporting game. We ignore the incentive-compatibility conditions for entre-

preneurs with zero returns; they turn out to be irrelevant in equilibrium.

While the model has only one active domestic lender, we suppose that there is potential

competition that forces the domestic lender to deliver all surplus to the entrepreneurs. This

potential competition implies that, regardless of the government’s choice of tax schedule,

the domestic lender gets only the reservation utility uL(2R). (More specifically, if the lender

gets more than that, a potential competitor will offer a loan contract with a lower FHH .)

Hence, an equilibrium contract (τ , F, L) maximizes the utility of the entrepreneurs, and is

any solution to the optimization problem:

max(τ,F,L)

(1− p)2[uE(BE (1− LHH) +RH − FHH)] + p(1− p)[uE(BE (1− LH0) +RH − FH0)]

+p(1− p)[uE(BE (1− L0H)− F0H)] + p2[uE(BE (1− L00)− F00)]

subject to (1), (2), an individual rationality constraint for the domestic lender:

(1− p)2uL(2(FHH + δLHH)− τ2) + 2p(1− p)uL(F0H + FH0 + δ(L0H + LH0)− τ1)(3)

+p2uL(2(F00 + δL00)− τ 0) = uL(2R)

and a zero-profit constraint for the foreign lenders:

(4) (1− p)2τ2 + 2p(1− p)τ1 + p2τ 0 ≥ RFORG

The last constraint says that the government’s expected repayments are enough to compensate

the foreign lenders for the initial loan of size G.

The following proposition provides a partial characterization of equilibrium contracts.

It shows that they look like debt contracts, with partial liquidations by the risk-averse entre-

preneurs when they default.

Proposition 1. Suppose (τ , F, L) is an equilibrium contract. Then:

14

1. FHH = FH0 > 0

2. If RH > FHH , then LHH = LH0 = 0

3. (τ , F, L) satisfies the incentive constraint (2) with equality

4. The zero profit constraint (4) is satisfied with equality

5. F00 = F0H = 0

6. 2R = 2(FHH + δLHH)− τ2 = F0H + FH0 + (δL0H + δLH0)− τ 1

= 2(F00 + δL00)− τ 0

Proof. Statement 1: Suppose FHH 6= FH0. Define a new bF which is the same as F exceptbFHH = bFH0 = (1− p)FHH + pFH0. Then, the entrepreneurs get higher utility with (τ , bF , L),because of the strict concavity of the objective. As well, (τ , bF , L) satisfies (1)-(4). Hence, inany equilibrium contract, FHH = FH0.

Statement 2: If LHH or LH0 are positive, we can increase the objective, without

violating the constraints, by lowering them by ε while increasing FHH and FH0 by ε.

Statement 3: Suppose the third statement is false. Given that the incentive-

compatibility constraint does not bind, the first order conditions for the equilibrium problem

imply that:

BE (1− LHH) +RH − FHH = BE (1− LH0) +RH − FH0

= BE (1− L0H)− F0H = BE (1− L00)− F00

But this violates the incentive constraint:

uE(BE (1− LHH)+RH−FHH) < (1−p)uE(BE (1− L0H)+R

H−F0H)+puE(BE (1− L00)+RH−F00)

Statement 4: If the fourth statement is false, we can lower τ2 by ε and lower FHH

by ε/2 without violating any of the constraints and increasing the objective; hence, in any

equilibrium the zero profit constraint holds with equality.

Statement 5: By (1), F00 and F0H are non-positive. To satisfy (2), we need that

F0j + L0j > 0 for at least one j. Suppose that F0H < 0 and L0H > 0. Define (bτ , bF, bL) to be a

15

contract that is the same as (τ , F, L) except:

bF0H = 0bL0H = L0H + F0H/BE

bτ1 = bF0H − F0H + δbL0H − δL0H + τ 1

The value of the objective under (bτ , bF, bL) is the same, and constraints (1), (2) and (3)are satisfied. The zero profit condition (4) is slack now:

(1− p)2τ 2 + 2p(1− p)³ bF0H − F0H + δ(bL0H − L0H) + τ 1

´+ p2τ 0

= RFORG− F0H2p(1− p)(1− δ/BE) > RFORG

>From the proof of Statement 4 above, we know that we can now lower τ 2 by ε and

lower FHH by ε/2 to improve the entrepreneurs’ objective. Hence, if F0H < 0, (τ , F, L) cannot

be an equilibrium, because (bτ , bF , bL) improves upon it. A similar argument can be used toshow that F00 < 0 cannot be an equilibrium.

Statement 6: Suppose this statement is false. Then, we can define:

τ 02 = 2(FHH + δLHH)− 2Rτ 01 = FH0 + F0H + (δL0H + δLH0)− 2Rτ 00 = 2(F00 + δL00)− 2R

The value of the objective has remained the same, and constraints (1), (2) and (3) are

satisfied. Because uL is strictly concave, we know that the expected value of the domestic

lender’s consumption is lower under τ 0:

(1− p)2(2(FHH + δLHH)− τ 02) + 2p(1− p)(FH0 + F0H + δL0H + δLH0 − τ 01)

+p2(2(F00 + δL00)− τ 00)

< (1− p)2(2(FHH + δLHH)− τ2) + 2p(1− p)(FH0 + F0H + δL0H + δLH0 − τ 1)

+p2(2(F00 + δL00)− τ 0)

16

This implies that:

(1− p)2τ 02 + 2p(1− p)τ 01 + p2τ 00

> (1− p)2τ 2 + 2p(1− p)τ1 + p2τ 0

>From the proof of Statement 4 above, we know that we can now lower τ 02 by ε and lower

FHH by ε/2 to improve the entrepreneurs’ objective. QED

The contracts described in Proposition 1 are essentially defaultable debt contracts. An

entrepreneur who announces a high return RH makes a positive repayment to the domestic

lender, and his capital is not liquidated. An entrepreneur who announces a low return makes

no payment to the domestic lender, and his capital is definitely partially liquidated. Thus,

announcing a low return is akin to deciding to default. Note that one entrepreneur’s contract

depends on the other’s default decision only through the level of liquidation. Note too that,

conditional on the entrepreneurs’ announced returns, there is no way to restructure payments

to make all participants better off. In this sense, the equilibrium contracts are renegotiation-

proof.

4. The Possibility of CrisesSuppose (τ , F, L) is an equilibrium contract. Given this contract, the two entrepreneurs

play a reporting game with one another in which they decide to report 0 or RH . Given the

nature of the equilibrium loan contract, we can interpret these choices as being to "default"

or "not to default" respectively. We noted above that the incentive-compatibility conditions

guarantee that if a successful entrepreneur chooses not to default, then it is optimal for the

other entrepreneur to make the same choice if successful. However, the incentive-compatibility

conditions do not rule out the possibility of other (strict) equilibria in this reporting game

between the entrepreneurs. Consider a putative equilibrium in which both entrepreneurs

decide to default when in fact they have high returns. This strategy forms a strict equilibrium

if:

uE(BE (1− L00) +RH) > uE(BE +RH − FH0)

17

(This condition exploits the result in Proposition 1 that LH0 = 0 and F00 = 0 in an equilibrium

contract.) In words, this condition says that an entrepreneur, with a high return, finds it

strictly optimal to default because he knows that the other entrepreneur is defaulting.14 We

shall call such an equilibrium a coordinated default crisis, and refer to contracts that allow

for such an equilibrium in the reporting game as being crisis contracts.

As the above description suggests, the constraint that caps aggregate liquidations plays

a fundamental role in generating crises. In particular, because F00 = F0H = 0, LHH = LH0 =

0, and FH0 = FHH , we know that in any equilibrium:

uE(BE +RH − FH0)

= (1− p)[uE(BE (1− L0H) +RH)] + p[uE(BE (1− L00) +RH)]

If L0H ≤ L00, then the equilibrium contract is not a crisis contract, because:

uE(BE +RH − FH0) ≥ uE(BE (1− L00) +RH)

It follows that crisis contracts arise only because L0H may be higher than L00.

We provide a sharp characterization of the conditions under which equilibrium con-

tracts are in fact crisis contracts. The key to this characterization is to understand when the

constraint L00 ≤ ξ/2 binds. The following proposition is useful in this regard.

Proposition 2. Suppose (τ , F, L) is an equilibrium contract such that L00 < ξ/2. Then:

L00 = L0H = L0 = FH/BE

Proof. Suppose (τ , F, L) is an equilibrium, but L0H 6= L00. Define the certainty equivalentbL0 so that:uE³BE

³1− bL0´+RH

´= (1− p)uE(BE (1− L0H) +RH) + puE(BE (1− L00) +RH)

14We assume that if entrepreneurs are indifferent between lying and telling the truth, they choose to tellthe truth. This (conventional) assumption implies that any crisis must necessarily be a strict equilibrium.

18

Define (bτ , bF , bL) to be a contract that is the same as (τ , F, L) except:bL00 = bL0H = bL0bτ1 = δbL0H − δL0H + τ 1

bτ0 = 2³δbL00 − δL00

´+ τ 0

Because uE exhibits non-increasing absolute risk aversion, we know that:

uE³BE

³1− bL0´´ > (1− p)uE(BE (1− L0H)) + puE(BE (1− L00))

and so the objective increases. Clearly, (bτ , bF , L) satisfies (1), (2), and (3).We also know that:(1− p)2τ 2 + 2p(1− p)bτ1 + p2bτ 0

= (1− p)2τ 2 + 2p(1− p)[δbL0H − δL0H + τ 1]

+p2[2δbL00 − 2δL00 + τ 0]

= RFORG+ 2pδ[bL0 − (1− p)L0H − pL00] > RFORG

where the last inequality is implied by the strict concavity of uE. Hence, if L0H 6= L00, (τ , F, L)

cannot be an equilibrium, because (bτ , bF , bL) improves upon it. The incentive constraint isthen: uE(BE +RH − FH) = uE

³BE

³1− bL0´+RH

´, and so bL0 = FH/BE. QED

The aggregate resources the lender gets from entrepreneurs are lower when either of

them defaults, because liquidation is a costly form of repayment. The taxes collected by the

government perfectly insure the domestic lender against this risk, which is then absorbed by

the foreign lender. Hence, the payments received by the foreign lender from the sovereign

borrower can be ordered as follows:

τ2 > τ 1 > τ 0

We treat τ2 as the face value of the sovereign debt. We say that a partial sovereign default

occurs if the foreign lender receives τ1 and a full sovereign default occurs if the foreign lender

receives τ 0.

19

We can use the above proposition to readily solve for the equilibrium contract, when

the upper bound on liquidation is non-binding. In that case, FH/BE = L0H = L00 = L∗0.

Hence, τ 2 = 2L∗0BE − 2R, τ 1 = δL∗0 − BEL∗0 − 2R, and τ0 = 2δL

∗0 − 2R. We can substitute

these taxes into the zero profit constraint of the foreign lender to obtain:

(1− p)2BEL∗0 + p(1− p)(BE + δ)L∗0 + p2δL∗0 = R+RFORG/2

which implies that equilibrium liquidation is given by:

(5) L∗0(R, p,G,RFOR, BE, δ) =

R+RFORG/2

(1− p)BE + pδ

This expression is useful in proving the following proposition that characterizes when

equilibrium contracts are in fact crisis contracts.

Proposition 3. If L∗0(R, p,G,RFOR, BE) ≤ ξ/2, then no equilibrium contracts are crisis

contracts. If L∗0(R, p,G,RFOR, BE) > ξ/2, then all equilibrium contracts are crisis contracts.

Proof. Suppose that:

L∗0(R, p,G,RFOR, BE, δ) ≤ ξ/2

Consider a relaxed version of the equilibrium contracting problem, without the upper bounds

on L0H and L00. As argued before the proposition, in any solution to this relaxed problem,

L0H = L00 = L∗0. Since L∗0 ≤ ξ/2, any solution to the relaxed problem is also a solution to

the original equilibrium contracting problem. Hence, in any equilibrium contract, FHH =

FH0 = BEL∗0, and L0H = L00 = L∗0. Given that L0H = L00, none of these contracts is a crisis

contract.

Now suppose that ξ is small enough such that L∗0(R, p,G,RFOR, BE) > ξ/2. In any

equilibrium contract (τ , F, L), FHH = FH0 = FH , and (FH , L0H , L00) satisfy:

(1− p)uE(BE(1− L0H) +RH) + puE(BE(1− L00) +RH) = uE(BE +RH − FH)

(1− p)FH + p(1− p)δL0H + p2δL00 = R+RFORG/2

20

(The first equality is the incentive constraint. The second equality is a combination of the

individual rationality and zero profit constraints.) We claim that this contract is a crisis

contract; that is, we claim L0H > L00. Suppose not. Then, ξ/2 ≥ L00 ≥ L0H . The incentive

constraint then implies that FH ≤ BEξ/2. Then, we can substitute into the zero profit

constraint to get:

(1− p)BEξ/2 + p(1− p)δξ/2 + p2δξ/2 ≥ R+RFORG/2

But this implies that:

ξ/2 ≥ R+RFORG/2

(1− p)BE + δp

which violates the hypothesized upper bound on ξ/2. It follows that all equilibrium contracts

are crisis contracts. QED

The idea behind the proposition is simple. If ξ is high enough, then the upper bound on

aggregate liquidation is basically irrelevant. It is possible to spread the equilibrium liquidation

across the two states in such a way that L00 is equal to L0H , which eliminates the possibility

of a coordinated default crisis. On the other hand, if ξ is low enough that the constraint on

aggregate liquidation binds, L00 must be less than L0H in equilibrium.

It is simple to show that to satisfy the domestic lender’s individual rationality con-

straint, it is necessary that L∗0(R, p,G,RFOR, BE, δ) > 1. Hence, Proposition 3 implies that

no equilibrium contract is a crisis contract if ξ = 2. Crises occur only because there is a

substantial constraint on aggregate liquidation.

In our model, liquidation provides a way to compensate the lenders and it provides a

way to discipline defaulting borrowers. Both roles matter in generating coordinated default

crises. If ξ is too low, then it is not possible to deliver a sufficiently strong punishment if

both borrowers default simultaneously. If δ is too low, then more liquidation is required to

satisfy the zero-profit-constraint of the lender. If the required amount of liquidation grows

to exceed ξ/2, then there is a possibility of coordinated default crises.

21

5. Crises and CorrelationsAbove we showed that for some parameter settings, under an equilibrium contract,

there is the possibility of a second equilibrium being played in the reporting game between

the entrepreneurs. However if this possibility is a real one, then the players, as Bayesians,

should assign a positive ex-ante probability to this equilibrium being played. Doing so will

affect the design of the original contract itself.

More specifically, suppose with probability ε, the entrepreneurs both privately observe

1 at the beginning of period 2, and with probability (1−ε), they both observe 0. These privatesignals allow the entrepreneurs to coordinate their reports. In particular, assume that it is

common knowledge that the entrepreneurs will default if they both observe 1 and if doing so

is a mutual best response, given a contract.15 We will call ε the sunspot probability.

As is typical in the coordination failure literature, we are silent about what the coordi-

nation device is. We think of the entrepreneurs as observing a number of independent payoff

irrelevant signals. (For example, the entrepreneurs observe exchange rates from a host of

countries other than their own.) They choose which of these signals to use as a coordination

device.

In this section, we examine the structure of equilibrium contracts, given that coordi-

nated default crises are positive probability events. We show that equilibrium rates of return

on domestic and sovereign foreign debt are positively correlated.

A. Positively Correlated Debt Returns

The common private signal mentioned above does not affect the nature of the feasibility

constraints (1) or incentive constraints (2). However, it does change the individual rationality

constraint (3), the zero profit constraint (4), and the objective of the entrepreneurs. The

15The lender could ask the entrepreneurs whether they have seen the sunspot or not. However, it is notpossible to design a contract which does not have an equilibrium in which they jointly claim not to have seenthe sunspot, but they actually have. For this reason, we do not bother to extend the contract to depend onthe sunspot.

22

individual rationality constraint becomes:

uL(2R) = (1− ε)(1− p)2uL(2(FHH + δLHH)− τ 2)

+2(1− ε)p(1− p)uL(F0H + FH0 + δL0H + δLH0 − τ1)

+[(1− ε)p2 + ε]uL(2(F00 + δL00)− τ 0)

The zero profit constraint becomes:

(1− ε)(1− p)2τ2 + 2(1− ε)p(1− p)τ1 + (p2(1− ε) + ε)τ 0 ≥ RFORG

Finally, the entrepreneur’s objective becomes:

(1− ε)(1− p)2uE(BE (1− LHH) +RH − FHH)

+(1− ε)p(1− p)uE(BE (1− LH0) +RH − FH0)

+(1− ε)p(1− p)uE(BE (1− L0H)− F0H) + [(1− ε)p2 + ε]uE(BE (1− L00)− F00)

An equilibrium contract, given sunspot probability ε, must maximize (the altered version of)

the entrepreneur’s objective subject to (1), (2) and the altered versions of (3) and (4).

Let (τ(ε), F (ε), L(ε)) be an equilibrium contract given sunspot probability ε. It is

straightforward to use the same logic as in Proposition 1 to establish the following character-

ization of (τ(ε), F (ε), L(ε)), for any ε ≥ 0.

Proposition 4. Suppose (τ (ε), F (ε), L(ε)) is an equilibrium contract given sunspot proba-

bility ε. Then:

23

1. FHH(ε) = FH0(ε) > 0

2. If RH > FHH(ε), then LHH(ε) = LH0(ε) = 0

3. (τ(ε), F (ε), L(ε)) satisfies the incentive constraint (2) with equality

4. τ(ε) satisfies the zero profit constraint (40) with equality

5. F0H(ε) = F00(ε) = 0

6. 2R = 2(FHH(ε) + δLHH(ε))− τ 2(ε) = F0H (ε) + FH0 (ε) + (δL0H (ε) + δLH0 (ε))− τ1(ε)

= 2(F00 (ε) + δL00 (ε))− τ0(ε)

Proof. The same as the proof of Proposition 1. QED

We know from Proposition 3 that crisis contracts exist only if ξ/2 is sufficiently small,

so that:

ξ/2 < L∗0(R, p,G,RFOR, BE, δ)

In the following proposition, we use this condition to prove that when sunspots are more

likely to occur, both domestic debt and sovereign foreign debt returns — that is, both FHH(ε)

and τ2(ε) — are higher.

Proposition 5. Define L∗0 as in (5) to be the equilibrium liquidation in a contract in which

the upper bound on liquidation does not bind (assuming ε = 0). Suppose that:

ξ/2 < L∗0(R, p,G,RFOR, BE, δ)

Then, for non-negative ε in a neighborhood of 0, FHH(ε) and τ 2(ε) are both strictly increasing

in ε.

Proof. In Appendix B.

This proposition shows that if ε increases, a non-defaulting entrepreneur will make a

bigger debt repayment to the domestic lender and the government will make a bigger debt

24

repayment to the foreign lender. Intuitively, when ε rises, the foreign lender is less likely to

receive the high repayment τ2. The foreign lender must be compensated for this probability

reduction with increased repayments by the government. This in turn calls for a larger

repayment of the non-defaulting entrepreneurs to the domestic lender.

The above assumes that the lender simply allows for the possibility of coordinated

default crises in offering a contract. The lender could instead restrict contracts to ones that

eliminate coordinated default crises entirely. To do so, we augment the original contractual

choice problem to include the constraint:

u(BE +RH − FH0) ≥ u(BE (1− L00) +RH)

or, equivalently, FH0 ≤ L00. Under the hypothesis of Proposition 3 about ξ, this constraint

must be binding. In the resultant contracts, FH0 < FHH . This extra randomness reduces

the value of the entrepreneur’s objective. However, the reduction is by an amount that is

independent of ε. It follows that, as long as ε is sufficiently small, this kind of random contract

is suboptimal relative to the one described in Proposition 5.

To sum up: low-probability sunspots affect the design of equilibrium contracts. In

particular, as the probability of a sunspot rises, the returns on domestic and foreign debt

both rise.

B. Real Exchange Rate Depreciations and Crises

In the data, sovereign debt crises are often associated with periods of real exchange

rate depreciation. Our model captures this connection in the following sense. In our model,

the domestic lender can lend to an entrepreneur or invest in an outside option. Suppose that

the utility of the lender is over wealth, and that the lender wants to maximize its wealth

to subsequently buy a bundle of tradable and nontradable goods. Furthermore, suppose

entrepreneurs are engaged in the production of nontradable goods, where incentive problems

are severe, while the lender’s outside opportunity consists of the production of tradable goods.

Under this interpretation, we can think of a depreciated real exchange rate as a rise in the

value of the tradable good production — that is, as an increase in R.

The following proposition shows that a rise in R can generate crises, when none existed

25

before.

Proposition 6. Define L∗0 as in (5) to be the equilibrium contract when the aggregate liqui-

dation constraint does not bind. Then:

∂L∗0(R, p,RFOR, G,BE, δ)

∂R> 0

Proof. Direct differentiation of (5) proves the result. QED.

Thus a rise in the outside option R can increase L∗0(R, p,G,RFOR, BE, δ) above ξ/2.

Proposition 3 implies that such a change can lead all equilibrium contracts to be crisis con-

tracts. We conclude that real exchange rate depreciations can generate sovereign and domestic

debt crises.

6. DiscussionIn this section, we discuss how we can enrich our model of sovereign default, whether

the global games approach is useful in eliminating the multiplicity of equilibria in the reporting

game, and how our results relate to those in the literature on international financial crises.

A. Enriching Our Model of Sovereign Default

In our model, the government must repay all loans. In reality, governments have a

choice over whether to do so or not, and indeed much of the literature on sovereign default

focuses on this choice. In this subsection, we consider two different ways to add such a choice

into the model. We argue that enriching the model in this way does not affect our results

greatly.

Ex-Post Participation Constraint

In our model, the sovereign has no ability to deviate from the recommendations of

the contract. Suppose instead that in period 2, the sovereign has the option to pay the

contractually mandated τ s or choose to face a sanction with exogenously specified cost k.

This option will impose an additional constraint on the equilibrium contracting problem

that τ s ≤ k for all s. Intuitively, this additional constraint will increase the amount of risk

each entrepreneur must bear in states when his announced return is RH . To satisfy the

26

incentive compatibility constraint of entrepreneurs, the contractually specified amount of

liquidation must increase. Thus, the ability of the sovereign to default increases the range of

the parameters consistent with equilibrium crisis contracts (just as increasing R or G does).

There is one empirical problem that emerges with this way of incorporating voluntari-

ness on the part of the sovereign. If the participation constraint binds, so that τ 2 = k, then

τ2 cannot vary with ε as in the prior section. Note that this empirically unattractive feature

arises because in this model of default, the sovereign is tempted to endure the sanction in

good times, not bad times.

Private Information About the Aggregate State

In the above simple model of sovereign default, the sanction k never occurs in equilib-

rium. Hence, in equilibrium, default is really still only a label that distinguishes repayment

states from one another. Consider the following distinct model of default. Suppose that as

above, it is possible to impose a sanction of cost k on the sovereign. In contrast to the above

model, though, we assume that the sovereign has full commitment and that τ s is privately

known to the sovereign.

The private information restriction will lead to an incentive-compatibility constraint

on the sovereign. In this model, in an equilibrium contract, the sovereign will pay k (with

some probability) for announcing values of s which lead to low repayments to the foreign

lender. As is true of the private debt contract in our benchmark model, we can interpret the

sovereign’s announcing a low value of s as being akin to declaring default.

This extra incentive constraint on the problem introduces even more risk to the entre-

preneurs, and so increases the amount of liquidation required. Again, this private-information

model of default expands the set of parameters consistent with equilibrium crisis contracts,

relative to our benchmark model. One attractive feature of this model is that, unlike the

prior participation-constraint model, the face value τ 2 is an increasing function of ε (the

probability of a coordinated default crisis).

B. Global Games: Getting Rid of the Multiplicity?

The problem in this economy is that there are two possible Bayesian-Nash equilibria in

the reporting game. In one equilibrium, both entrepreneurs tell the truth. In the other, they

27

coordinate on lying by claiming to be unsuccessful even when they are successful. In the past

fifteen years, international economists have made effective use of global games refinements to

eliminate multiplicities that emerge models of currency crises (Morris and Shin (1998)). Can

these methods be used to the same effect in our setting?

The essence of the global games approach is that we pick the equilibrium which best

approximates equilibrium play in a perturbed game which has small private signals about the

payoffs. In that way, we can understand which equilibrium is more robust to deviations from

common knowledge about those payoffs. But in our contracting setup, the lender writes down

a contract that specifies FH , L0H , and L00. Why would these numbers then be anything less

than common knowledge among the two entrepreneurs? To us, the lack of common knowledge

of payoffs that underlies the global games approach seems strained in our setting.16

C. Relationship to the International Financial Crises Literature

In the introduction, we discussed the relationship between our paper and the existing

theories of sovereign defaults. Our paper is also related to the broader literature that discusses

how financial frictions can generate and exacerbate international financial crises. The papers

in this literature have modelled a wide variety of financial frictions. Several papers emphasize

that, especially in bad times, domestic banks/borrowers may run short on collateral that

is acceptable to foreign lenders (Caballero and Krishnamurthy (2001); Chang and Velasco

(2001)17). Without this collateral, domestic agents face what is often termed a sudden stop

to their borrowing from abroad. Other papers stress the role of what are termed balance

sheet effects. These models assume that exchange rate movements are unhedged. Then,

16It may still seem plausible to some readers that the two entrepreneurs’ strategies are not common knowl-edge (as is assumed in a Bayesian-Nash equilibrium). What happens if we relax the common knowledgeassumption in an ad hoc fashion? Note that of the two equilibria under consideration, the truth-telling equi-librium is actually less robust. We only consider the lying equilibrium if it is in fact a strict equilibrium.But the truth-telling equilibrium is necessarily not strict because the incentive constraint holds with equal-ity. Clearly, without much loss in utility to the entrepreneurs, the lender could alter the contract slightly,so that truth-telling is a strict equilibrium. Nonetheless, under these slightly altered contracts, the lyingequilibrium still risk-dominates the truth-telling equilibrium. As Carlsson and van Damme (1993) argue, therisk-dominant equilibrium survives a wider class of deviations from common knowledge and is the one pickedout by a global games refinement.17Chang and Velasco (2001) also highlight the role of foreign creditors in generating financial crises. In

their model, runs on domestic deposits may interact with foreign creditor panics, depending on the maturityof the foreign debt and the liquidity of domestic banks. As we noted in footnote 6, bank runs play no role ingenerating the internal debt crises in our data.

28

sudden devaluations decrease the value of domestic assets, generating insufficient funds and

bankruptcies (Schneider and Tornell (2004)). Finally, in most, if not all, of these papers,

crises could be eliminated or ameliorated by better government policy. In particular, many

authors have been sharply critical of policies that commit the domestic government to bail

out domestic banks or entrepreneurs.

Our paper differs from this prior literature in two important respects. First, in these

earlier papers, the various crises emerge at least in part because the country is involved in

international financial markets. In our paper, crises occur only because of the upper bound on

liquidation. Hence, changes in the perceived probability of coordinated defaults can generate

sharp spikes in domestic interest rates even if the country were not able to borrow and lend

from overseas. It is true — of course — that sovereign default can only occur in our model

because the country is able to borrow from abroad. But this possibility of sovereign default

is only beneficial, because it allows the country to insure itself against domestic shocks.

Second, and related, the existing literature points to government’s bad policies in the

form of bailout guarantees as being a source of crises (Burnside, Eichenbaum and Rebelo

(2004)). We construct a contractual arrangement that is Pareto optimal, given the upper

bound on liquidation. If its debt level is relatively small, government bailout guarantees

are part of an ex-ante optimal arrangement. Intuitively, private agents interact with foreign

lenders/insurers only through their government. Because the foreign lenders are risk-neutral,

they provide transfers of resources to the home country when the country is doing poorly.

These transfers flow through the government to the private sector. They are, in fact, (partial)

bailouts. Analyzing debt crises within an optimal contracting structure allows us to pinpoint

precisely the source of crises. Within our framework, improving financial and legal institutions

domestically to resolve large-scale defaults is the only way to reduce the probability of crises.

7. ConclusionsIn this paper, we use data from developing countries to argue that sovereign debt

and domestic debt default risk are tightly linked. We find a strong correlation in ex-ante

measures of default risk as well as ex-post default events in international sovereign loans

and private domestic loans. We use both temporal and country-specific evidence to establish

29

that the domestic defaults cause the sovereign defaults, not the other way around. We find

that widespread domestic defaults are generated by non-fundamental shocks. The resulting

domestic default crises then place great fiscal pressure on governments, leading at times to

defaults on foreign loans. We develop a simple model of these phenomena. The model shows

that, given aggregate constraints on liquidation, these kinds of crises are an inevitable part

of an optimal response to informational problems in private-sector lending.

In our model, outcomes would be improved if it were possible to increase the exogenous

parameter ξ (the upper bound on aggregate liquidation). In reality, this parameter is certainly

endogenous, and is determined by complex politico-economic forces. Understanding these

forces, and how to control them through better institutional design, is an important avenue

for future research.

30

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33

Appendix AIn this appendix we provide details on the data sources, series and default events dates

used in the Section 2.

Default Risk Data

Private default risk is calculated as follows. For Argentina, Ecuador, Indonesia,

Panama, Peru, Poland, Russia, and Ukraine, we use the spread between dollar average

domestic lending rate and the yield U.S. Treasury of 1 year maturity. For Brazil, Chile,

Colombia, Korea, Malaysia, Mexico, Nigeria, Philippines, Thailand, and Venezuela, we use

the spread between the average local currency domestic lending rate and the average local

currency domestic deposit rate.

Sovereign default risk is the EMBI+ spread for Argentina, Brazil, Colombia, Ecuador,

Mexico, Nigeria, Panama, Peru, Philippines, Poland, Russia, Ukraine, and Venezuela. The

additional five countries do not have EMBI+ spreads. These are the series used for them.

Chile: Inflation Indexed 10-year Bond Yield relative to the Inflation Indexed deposit rate

denominated in Chilean Peso, Indonesia: Spread of 7.75% Notes of 08-01-2006 denominated

in U.S. Dollars relative to yield of a 1 year U.S. Treasury, Korea: 5-year Government Bond

denominated in Korean South Won relative to the average deposit rate, Malaysia: 10-year

Government Bond Yield denominated in Malaysia Dollar relative to the average deposit rate,

Thailand: 10-year Government Bond Yield denominated in Thailand Baht relative to the

average deposit rate.

All the data come from the Global Financial Statistics Database and the International

Financial Statistics at the IMF except for the series on dollar lending rates for Poland and

Russia that come from each country’s Central Bank.

Dates of Sovereign Defaults and Internal Debt Crises

The following table reports the dates of sovereign defaults and internal debt crises.

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Table 3: Crisis Dates

Sovereign Defaults Internal Debt Crises

Argentina 82-93, 89, 01-04 80-82, 89, 95, 01-04Brazil 83-94 90, 94-99Chile 83-90 81-83Colombia 82-87Ecuador 85-95, 99-00 80-83, 95-97, 98-02Indonesia 98-00, 02 94, 97—02Korea 97-02Malaysia 85-88, 97-01Mexico 82-90 81-91, 94-00Nigeria 82-92, 86-88, 92, 02 92-97Panama 83-96, 87-94 88-89Peru 80, 84-97 83-90Philippines 83-92 81-87, 98-02Poland 81-94 90-95Russia 91-97, 98-00 95, 98-99Thailand 83-87, 97-02Ukraine 98-00 97-98Venezuela 83-88, 90, 95-97 81-86, 94-95

Appendix BIn this appendix, we provide a proof of Proposition 5.

We first prove that there is a neighborhood of 0 such that there is a unique equilibrium

contract for all ε ≥ 0. We start with ε = 0. Suppose that the equilibrium contract was such

that the constraint on aggregate liquidation does not bind. Then, the equilibrium contract’s

payments would be given by:

FHH = FH0 = BEL∗0(R, p,G,R

FOR, BE, δ)

L0H = L00 = L∗0(R, p,G,RFOR, BE, δ)

But this contract exceeds the upper bound on aggregate liquidation (because 2L00 exceeds ξ),

and cannot be an equilibrium contract. It follows that there is a unique equilibrium contract

35

(τ , F, L):

FHH = FH0 = bFH

F00 = F0H = LH0 = LHH = 0

L0H = bL0H , L00 = δ−1ξ/2

τ 2 = 2 bFH − 2Rτ 1 = bFH + δbL0H − 2Rτ 0 = ξ − 2R

where ( bFH , bL0H) is the unique solution to:uE(BE +RH − bFH) = (1− p)uE

³BE

³1− bL0H´+RH

´+ puE(BE (1− ξ/2) +RH)

(1− p) bFH + δp(1− p)bL0H + p2ξ/2 = R +RFORG/2

Now suppose ε > 0. By the Theorem of the Maximum, there is a unique equilibrium contract

for ε near 0, and that contract’s (F,L) satisfies:

uE(BE +RH − FH)− (1− p)uE(BE (1− L0H) +RH)− puE(BE (1− ξ/2) +RH) = 0(6)

[p2(1− ε) + ε]ξ/2 + δp(1− p)(1− ε)L0H + (1− p)(1− ε)FH = R+RFORG/2(7)

For notational convenience, we’ve set FH = FHH = FH0 and suppressed the dependence of

the payments on ε. Using the implicit function theorem, we can show that FH is continuously

differentiable in ε for ε near 0. Differentiating (6) and (7) with respect to ε, around ε = 0,

we get:

(1− p)u0E³BE

³1− bL0H´+RH

´BEL

00H(0) = u0E(BE +RH − bFH)F

0H(0)

p(1− p)δL00H(0) + (1− p)F 0H(0) = R+RFORG/2− ξ/2

36

Substituting the first equation into the second, we get:

pδu0E(BE +RH − bFH)

u0E(BE

³1− bL0H´+RH)BE

F 0H(0) + (1− p)F 0H(0) = R +RFORG/2− ξ/2

which implies that F 0H(0) > 0. Since FH is C1 for ε near 0, we can conclude that F 0H(ε) > 0

for ε in a neighborhood of zero.

Proof. >From Proposition 3, we know that:

τ2(ε) = 2FH(ε)− 2R

and so τ 02(ε) > 0. QED

37